This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here are the numbers whose logarithms are given: The antilogarithm of a number x is 10^x. For logarithms with a bar notation, e.g., 1.8056, it means -1 + 0.8056. a) For 0.3760: Step 1: Calculate the antilogarithm. 10^0.3760 ≈ 2.377 The number is 2.377. b) For 0.7783: Step 1: Calculate the antilogarithm. 10^0.7783 ≈ 6.003 The number is 6.003. c) For 1.6415: Step 1: Calculate the antilogarithm. 10^1.6415 ≈ 43.80 The number is 43.80. d) For 1.1127: Step 1: Calculate the antilogarithm. 10^1.1127 ≈ 13.05 The number is 13.05. e) For 1.9364: Step 1: Calculate the antilogarithm. 10^1.9364 ≈ 86.39 The number is 86.39. f) For 2.8579: Step 1: Calculate the antilogarithm. 10^2.8579 ≈ 721.0 The number is 721.0. g) For 2.8835: Step 1: Calculate the antilogarithm. 10^2.8835 ≈ 764.7 The number is 764.7. h) For 3.5104: Step 1: Calculate the antilogarithm. 10^3.5104 ≈ 3239 The number is 3239. i) For 1.8056: Step 1: Rewrite the logarithm. 1.8056 = -1 + 0.8056 Step 2: Calculate the antilogarithm. 10^-1 + 0.8056 = 10^0.8056 × 10^-1 ≈ 6.392 × 10^-1 = 0.6392 The number is 0.6392. j) For 1.7194: Step 1: Rewrite the logarithm. 1.7194 = -1 + 0.7194 Step 2: Calculate the antilogarithm. 10^-1 + 0.7194 = 10^0.7194 × 10^-1 ≈ 5.241 × 10^-1 = 0.5241 The number is 0.5241. k) For 2.5518: Step 1: Rewrite the logarithm. 2.5518 = -2 + 0.5518 Step 2: Calculate the antilogarithm. 10^-2 + 0.5518 = 10^0.5518 × 10^-2 ≈ 3.563 × 10^-2 = 0.03563 The number is 0.03563. l) For 3.2052: Step 1: Rewrite the logarithm. 3.2052 = -3 + 0.2052 Step 2: Calculate the antilogarithm. 10^-3 + 0.2052 = 10^0.2052 × 10^-3 ≈ 1.604 × 10^-3 = 0.001604 The number is 0.001604. That's 2 down. 3 left today — send the next one.